First slide

Theory of equations

Question

If the equation $2 x^{2} + 3 x + 5 λ = 0 and x^{2} + 2 x + 3 λ = 0$ have a common root, then $λ$ s equal to

Moderate

A

0
B

-1
C

0 ,-1
D

2 ,-1

Solution

Given equations are $2 x^{2} + 3 x + 5 λ = 0$ and $x^{2} + 2 x + 3 λ = 0$ have a common root, if
$\frac{x^{2}}{(9 - 10) λ} = \frac{x}{(5 - 6) λ} = \frac{1}{(4 - 3)} \begin{array}{ll} \Rightarrow \frac{x^{2}}{- λ} = \frac{x}{- λ} = \frac{1}{1} \\ \Rightarrow x^{2} = - λ, x = - λ or λ = - 1, 0 \end{array}$

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